Malcolm, am I right in observing that the feminine name "L(o)u" is almost unheard of in British Isles folksong ? I can't think of any American "folk-type verse" occurrences aside from Robert Service's once fabulously well known "Shooting of Dan McGrew" (~1902).

In America, "Liza" occurs rarely, mostly in minstrel songs. ("Lulu" is at least equally rare.) My suggestion is that MacDonagh wrote that stanza.